This paper shows a physically cogent model for electrical noise in resistors that has been obtained from Thermodynamical reasons. This new model derived from the works of Johnson and Nyquist also agrees with the Quant...This paper shows a physically cogent model for electrical noise in resistors that has been obtained from Thermodynamical reasons. This new model derived from the works of Johnson and Nyquist also agrees with the Quantum model for noisy systems handled by Callen and Welton in 1951, thus unifying these two Physical viewpoints. This new model is a Complex or 2-D noise model based on an Admittance that considers both Fluctuation and Dissipation of electrical energy to excel the Real or 1-D model in use that only considers Dissipation. By the two orthogonal currents linked with a common voltage noise by an Admittance function, the new model is shown in frequency domain. Its use in time domain allows to see the pitfall behind a paradox of Statistical Mechanics about systems considered as energy-conserving and deterministic on the microscale that are dissipative and unpredictable on the macroscale and also shows how to use properly the Fluctuation-Dissipation Theorem.展开更多
This paper shows that today’s modelling of electrical noise as coming from noisy resistances is a non sense one contradicting their nature as systems bearing an electrical noise. We present a new model for electrical...This paper shows that today’s modelling of electrical noise as coming from noisy resistances is a non sense one contradicting their nature as systems bearing an electrical noise. We present a new model for electrical noise that including Johnson and Nyquist work also agrees with the Quantum Mechanical description of noisy systems done by Callen and Welton, where electrical energy fluctuates and is dissipated with time. By the two currents the Admittance function links in frequency domain with their common voltage, this new model shows the connection Cause-Effect that exists between Fluctuation and Dissipation of energy in time domain. In spite of its radical departure from today’s belief on electrical noise in resistors, this Complex model for electrical noise is obtained from Nyquist result by basic concepts of Circuit Theory and Thermo-dynamics that also apply to capacitors and inductors.展开更多
The origin of the Johnson noise of resistors is reviewed by a new model fitting in the Fluctuation-Dissipation framework and compared with the velocity noise in Brownian motion. This new model handling both fluctuatio...The origin of the Johnson noise of resistors is reviewed by a new model fitting in the Fluctuation-Dissipation framework and compared with the velocity noise in Brownian motion. This new model handling both fluctuations as well as dissipations of electrical energy in the Complex Admittance of any resistor excels current model based on the dissipation in their conductance. From the two orthogonal currents associated to a sinusoidal voltage in an electrical admittance, the new model that also considers the discreteness of the electrical charge shows a Cause-Effect dynamics for electrical noise. After a brief look at systems considered as energy-conserving and deterministic on the microscale that are dissipative and unpredictable on the macroscale, the arrow of time is discussed from the noise viewpoint.展开更多
By a Quantum-compliant model for electrical noise based on Fluctuations and Dissipations of electrical energy in a Complex Admittance, we will explain the phase noise of oscillators that use feedback around L-C resona...By a Quantum-compliant model for electrical noise based on Fluctuations and Dissipations of electrical energy in a Complex Admittance, we will explain the phase noise of oscillators that use feedback around L-C resonators. Under this new model that departs markedly from current one based on energy dissipation in Thermal Equilibrium (TE), this dissipation comes from a random series of discrete Dissipations of previous Fluctuations of electrical energy, each linked with a charge noise of one electron in the Capacitance of the resonator. When the resonator out of TE has a voltage between terminals, a discrete Conversion of electrical energy into heat accompanies each Fluctuation to account for Joule effect. This paper shows these Foundations on electrical noise linked with basic skills of electronic Feedback to be used in a subsequent paper where the aforesaid phase noise is explained by the new Admittance-based model for electrical noise.展开更多
Using a new Admittance-based model for electrical noise able to handle Fluctuations and Dissipations of electrical energy, we explain the phase noise of oscillators that use feedback around L-C resonators. We show tha...Using a new Admittance-based model for electrical noise able to handle Fluctuations and Dissipations of electrical energy, we explain the phase noise of oscillators that use feedback around L-C resonators. We show that Fluctuations produce the Line Broadening of their output spectrum around its mean frequency f0 and that the Pedestal of phase noise far from f0 comes from Dissipations modified by the feedback electronics. The charge noise power 4FkT/R C2/s that disturbs the otherwise periodic fluctuation of charge these oscillators aim to sustain in their L-C-R resonator, is what creates their phase noise proportional to Leeson’s noise figure F and to the charge noise power 4kT/R C2/s of their capacitance C that today’s modelling would consider as the current noise density in A2/Hz of their resistance R. Linked with this (A2/Hz?C2/s) equivalence, R becomes a random series in time of discrete chances to Dissipate energy in Thermal Equilibrium (TE) giving a similar series of discrete Conversions of electrical energy into heat when the resonator is out of TE due to the Signal power it handles. Therefore, phase noise reflects the way oscillators sense thermal exchanges of energy with their environment.展开更多
文摘This paper shows a physically cogent model for electrical noise in resistors that has been obtained from Thermodynamical reasons. This new model derived from the works of Johnson and Nyquist also agrees with the Quantum model for noisy systems handled by Callen and Welton in 1951, thus unifying these two Physical viewpoints. This new model is a Complex or 2-D noise model based on an Admittance that considers both Fluctuation and Dissipation of electrical energy to excel the Real or 1-D model in use that only considers Dissipation. By the two orthogonal currents linked with a common voltage noise by an Admittance function, the new model is shown in frequency domain. Its use in time domain allows to see the pitfall behind a paradox of Statistical Mechanics about systems considered as energy-conserving and deterministic on the microscale that are dissipative and unpredictable on the macroscale and also shows how to use properly the Fluctuation-Dissipation Theorem.
文摘This paper shows that today’s modelling of electrical noise as coming from noisy resistances is a non sense one contradicting their nature as systems bearing an electrical noise. We present a new model for electrical noise that including Johnson and Nyquist work also agrees with the Quantum Mechanical description of noisy systems done by Callen and Welton, where electrical energy fluctuates and is dissipated with time. By the two currents the Admittance function links in frequency domain with their common voltage, this new model shows the connection Cause-Effect that exists between Fluctuation and Dissipation of energy in time domain. In spite of its radical departure from today’s belief on electrical noise in resistors, this Complex model for electrical noise is obtained from Nyquist result by basic concepts of Circuit Theory and Thermo-dynamics that also apply to capacitors and inductors.
文摘The origin of the Johnson noise of resistors is reviewed by a new model fitting in the Fluctuation-Dissipation framework and compared with the velocity noise in Brownian motion. This new model handling both fluctuations as well as dissipations of electrical energy in the Complex Admittance of any resistor excels current model based on the dissipation in their conductance. From the two orthogonal currents associated to a sinusoidal voltage in an electrical admittance, the new model that also considers the discreteness of the electrical charge shows a Cause-Effect dynamics for electrical noise. After a brief look at systems considered as energy-conserving and deterministic on the microscale that are dissipative and unpredictable on the macroscale, the arrow of time is discussed from the noise viewpoint.
文摘By a Quantum-compliant model for electrical noise based on Fluctuations and Dissipations of electrical energy in a Complex Admittance, we will explain the phase noise of oscillators that use feedback around L-C resonators. Under this new model that departs markedly from current one based on energy dissipation in Thermal Equilibrium (TE), this dissipation comes from a random series of discrete Dissipations of previous Fluctuations of electrical energy, each linked with a charge noise of one electron in the Capacitance of the resonator. When the resonator out of TE has a voltage between terminals, a discrete Conversion of electrical energy into heat accompanies each Fluctuation to account for Joule effect. This paper shows these Foundations on electrical noise linked with basic skills of electronic Feedback to be used in a subsequent paper where the aforesaid phase noise is explained by the new Admittance-based model for electrical noise.
文摘Using a new Admittance-based model for electrical noise able to handle Fluctuations and Dissipations of electrical energy, we explain the phase noise of oscillators that use feedback around L-C resonators. We show that Fluctuations produce the Line Broadening of their output spectrum around its mean frequency f0 and that the Pedestal of phase noise far from f0 comes from Dissipations modified by the feedback electronics. The charge noise power 4FkT/R C2/s that disturbs the otherwise periodic fluctuation of charge these oscillators aim to sustain in their L-C-R resonator, is what creates their phase noise proportional to Leeson’s noise figure F and to the charge noise power 4kT/R C2/s of their capacitance C that today’s modelling would consider as the current noise density in A2/Hz of their resistance R. Linked with this (A2/Hz?C2/s) equivalence, R becomes a random series in time of discrete chances to Dissipate energy in Thermal Equilibrium (TE) giving a similar series of discrete Conversions of electrical energy into heat when the resonator is out of TE due to the Signal power it handles. Therefore, phase noise reflects the way oscillators sense thermal exchanges of energy with their environment.
